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In any case, receiver (Coinbase) can't do much to make your transaction confirm faster. Except CPFP, but you can do the same with your change output, if you have it. But, as mentioned above, if tx fee really is 0, it will not be relayed by the network, as default relay fee is 1 satoshi per vbyte. Also, in 7 days it should have been confirmed, as mempool ...


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When you add a very small fee or no fee at all, as in your case, you'll need to ask for a special favor from a mining pool in order to get your TX in. It is possible to request, on exceptional basis, for a mining pool to include your transaction into one of their less busy blocks. They call this service "transaction accelerators". For instance, ViaBTC ...


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